This doesn’t follow and is false. The set difference operation is well-defined, so the result is not logical nonsense. The corresponding set cardinalities after a specific set difference will also be well-defined, since the cardinality function is also well-defined.
To clarify the contradiction I mentioned above, if n denotes the cardinality operator, v the disjunction operator, ^ the conjunction operator, O the set of odd numbers, E the set of even numbers, ES the empty set, n(ES) = 0, and n(O) = n(E) = inf:
If I give both bags to you, I will keep no bags, and therefore will have zero marbles:
A1: n((O v E)\(O v E)) = n(O v E) - n((O v E) ^ (O v E)) = n(O v E) - n(O v E) = inf—inf.
B1: n((O v E)\(O v E)) = n(ES) = 0.
C1: A1^ B1 ⇒ inf—inf = 0.
If I give 1 bag to you, I will keep 1 bag, and therefore will have infinite marbles:
A2: n((O v E)\O) = n(O v E) - n((O v E) ^ O) = n(O v E) - n(O) = inf—inf.
B2: n((O v E)\O) = n((O v E)\E) = n(O) = inf.
C2: A2 ^ B2 ⇒ inf—inf = inf.
So there is a contradiction:
D: C1 ^ C2 ⇒ 0 = inf.
Since, 0 = inf is false, one of the following is false:
The relationship R ⇔ n(X\Y) = n(X) - n(X ^ Y), which I used above, exists in the real world.
Infinites exist in the real world.
I guess you would be inclined towards putting non-null weight into each one of these points being false. However, R essentially means the whole is the sum of its parts, which I cannot see being false in the real world. So I reject the existence of infinites in the real world.
To clarify the contradiction I mentioned above, if n denotes the cardinality operator, v the disjunction operator, ^ the conjunction operator, O the set of odd numbers, E the set of even numbers, ES the empty set, n(ES) = 0, and n(O) = n(E) = inf:
If I give both bags to you, I will keep no bags, and therefore will have zero marbles:
A1: n((O v E)\(O v E)) = n(O v E) - n((O v E) ^ (O v E)) = n(O v E) - n(O v E) = inf—inf.
B1: n((O v E)\(O v E)) = n(ES) = 0.
C1: A1^ B1 ⇒ inf—inf = 0.
If I give 1 bag to you, I will keep 1 bag, and therefore will have infinite marbles:
A2: n((O v E)\O) = n(O v E) - n((O v E) ^ O) = n(O v E) - n(O) = inf—inf.
B2: n((O v E)\O) = n((O v E)\E) = n(O) = inf.
C2: A2 ^ B2 ⇒ inf—inf = inf.
So there is a contradiction:
D: C1 ^ C2 ⇒ 0 = inf.
Since, 0 = inf is false, one of the following is false:
The relationship R ⇔ n(X\Y) = n(X) - n(X ^ Y), which I used above, exists in the real world.
Infinites exist in the real world.
I guess you would be inclined towards putting non-null weight into each one of these points being false. However, R essentially means the whole is the sum of its parts, which I cannot see being false in the real world. So I reject the existence of infinites in the real world.